Multilevel Holstein-Primakoff approximation and its application to atomic spin squeezing and ensemble quantum memories

We show that an ensemble of identical d-level atoms can be efficiently described by d-1 collective oscillator degrees of freedom in the vicinity of a product state with all atoms in the same, but otherwise arbitrary single-particle state. We apply our description to two different kinds of spin squeezing: (i) when each spin-F atom is individually squeezed without creating interatomic entanglement and (ii) when a particular collective atomic oscillator mode is squeezed via quantum non-demolition (QND) measurement and feedback. When combined in sequence, the order of the two methods is relevant in the final degree of squeezing. We also discuss the role of the two kinds of squeezing when multi-sublevel atoms are used as quantum memories for light.Comment: 12 pages, 3 figure

General criterion for oblivious remote state preparation

A necessary and sufficient condition is given for general exact remote state preparation (RSP) protocols to be oblivious, that is, no information about the target state can be retrieved from the classical message. A novel criterion in terms of commutation relations is also derived for the existence of deterministic exact protocols in which Alice's measurement eigenstates are related to each other by fixed linear operators similar to Bob's unitaries. For non-maximally entangled resources, it provides an easy way to search for RSP protocols. As an example, we show how to reduce the case of partially entangled resources to that of maximally entangled ones, and we construct RSP protocols exploiting the structure of the irreducible representations of Abelian groups.Comment: 5 pages, RevTe

Parametric amplification of the mechanical vibrations of a suspended nanowire by magnetic coupling to a Bose-Einstein condensate

We consider the possibility of parametric amplification of a mechanical vibration mode of a nanowire due to its interaction with a Bose-Einstein condensate (BEC) of ultracold atoms. The magneto-mechanical coupling is mediated by the vibrationally modulated magnetic field around the current-carrying nanowire, which can induce atomic transitions between different hyperfine sublevels. We theoretically analyze the limitations arising from the fact that the spin inverted atomic medium which feeds the mechanical oscillation has a finite bandwidth in the range of the chemical potential of the condensate

Quantized recurrence time in iterated open quantum dynamics

The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of systems that includes classical Markov chains and unitary discrete time quantum walks on networks. Starting from a pure state, the time evolution is induced by repeated applications of a general quantum channel, in each timestep followed by a measurement to detect whether the system has returned to the original state. We prove that if the superoperator is unital in the relevant Hilbert space (the part of the Hilbert space explored by the system), then the expectation value of the return time is an integer, equal to the dimension of this relevant Hilbert space. We illustrate our results on partially coherent quantum walks on finite graphs. Our work connects the previously known quantization of the expected return time for bistochastic Markov chains and for unitary quantum walks, and shows that these are special cases of a more general statement. The expected return time is thus a quantitative measure of the size of the part of the Hilbert space available to the system when the dynamics is started from a certain state

Continuous variable remote state preparation

We extend exact deterministic remote state preparation (RSP) with minimal classical communication to quantum systems of continuous variables. We show that, in principle, it is possible to remotely prepare states of an ensemble that is parameterized by infinitely many real numbers, i.e., by a real function, while the classical communication cost is one real number only. We demonstrate continuous variable RSP in three examples using (i) quadrature measurement and phase space displacement operations, (ii) measurement of the optical phase and unitaries shifting the same, and (iii) photon counting and photon number shift.Comment: 7 pages, RevTeX

Continuous variable versus EIT-based quantum memories

We discuss a general model of a quantum memory for a single light mode in a collective mode of atomic oscillators. The model includes interaction Hamiltonians that are of second order in the canonical position and momentum operators of the light- and atomic oscillator modes. We also consider the possibility of measurement and feedback. We identify an interaction Hamiltonian that leads to an ideal mapping by pure unitary evolution and compare several schemes which realize this mapping using a common continuous-variable description. In particular we discuss schemes based on the off-resonant Faraday effect supplemented by measurement and feedback and proper preparation of the atoms in a squeezed state and schemes based on off-resonant Raman coupling as well as electromagnetically induced transparency (EIT).Comment: 12 pages, 4 figure

Qubit Protection in Nuclear-Spin Quantum Dot Memories

We present a mechanism to protect quantum information stored in an ensemble of nuclear spins in a semiconductor quantum dot. When the dot is charged the nuclei interact with the spin of the excess electron through the hyperfine coupling. If this coupling is made off-resonant it leads to an energy gap between the collective storage states and all other states. We show that the energy gap protects the quantum memory from local spin-flip and spin-dephasing noise. Effects of non-perfect initial spin polarization and inhomogeneous hyperfine coupling are discussed.Physic